# Circle A has a center at #(1 ,7 )# and a radius of #1 #. Circle B has a center at #(-3 ,-2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

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The circles do not overlap. The smallest distance between them is the difference between the distance of their centers and the sum of their radii, which is ( \sqrt{(1 - (-3))^2 + (7 - (-2))^2} - (1 + 2) = \sqrt{25 + 81} - 3 = \sqrt{106} - 3 \approx 7.3 - 3 = 4.3 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(4 ,9 )# to #(8 ,5 )# and the triangle's area is #34 #, what are the possible coordinates of the triangle's third corner?
- A line passes through #(3 ,2 )# and #(5 ,3 )#. A second line passes through #(7 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- What is the equation of a line perpendicular to the line #y-2x=5# and goes through (1,2)?
- A triangle has corners at #(9 ,3 )#, #(4 ,4 )#, and #(3 ,7 )#. How far is the triangle's centroid from the origin?
- Circle A has a center at #(-1 ,-4 )# and a radius of #3 #. Circle B has a center at #(-3 ,2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

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